Time to get into the fray.

>>not expecting a lost queen. The hive goes into emergency mode and 3-4 days
>>later you'll find, but few take the time to look, sealed queen cells.

I have not seen sealed queen cells 3 or 4 days after sudden loss of a
queen.  I have never knowingly checked a hive at that time after it became
queenless.  If I am making a split, or adding young brood to a queenless
hive etc., I make it a point not to disturb them for around ten days.

>>        It takes 3 days to hatching, so those sealed at 3 days after
emergency
>>only get a 6 day feeding, instead of 9 which is normal.

>A normal queen larva is fed for only 5 days, (3 days as an egg, 5 days
>unsealed, 8 days sealed).

My understanding has always been that the hive can turn any young worker
larvae, ( less than three days old), into a queen.  If the bees start to
work on a larvae of that age, a sealed queen cell at 3-4 days after
becoming queenless is quite possible.  I do not agree with the idea that
the hive (or its circumstances) can alter the normal time for queen
development.  There are  factors that I am aware of that  can change an
insect's development time.  Some of them would be temperature (warmer may
tend to speed it a little, cooler may tend to slow it), some hormones such
as are used in some pesticides to delay an insect's development into an
adult until it "burns itself out" (my terminology, not the entomologist's),
and some circumstances (for which I don't know the trigger') where insects
go into an extended diapause, as happens with some corn pests which don't
emerge as adults in the normal time, but the next season instead (about a
year later).
There may be more, and I do not mean to rule out the possibility that bees
have the ability to alter development time, only that I haven't seen or
heard of it, and do not think they can or do.  This would not include the
hive that keeps a queen in her cell after she could have emerged.  She has
already developed, she's just being prevented from emerging.
I think the question (that David has addressed) is how important are those
first three days as a larvae in queen development (assuming that 3 day old
larvae may be raised into a queen).  David, it appears, feels that this is
a critical  time for the development of a commercially good queen.  He
could very well be correct.  Even if this early larval stage is critical to
good queen development, there will be times that larvae will receive better
care due to larger numbers of nurse bees, good or bad weather, honey flow
etc.  and these may already have had everything they need to become a very
good queen.
 Sorry I ramble.
Bill